Question

Find the relative molecular mass of a gas, 0.546 g of which occupies 360 cm³ at 87°C and 380 mm $\mathrm{Hg}$ pressure. [1 litre of hydrogen at S.T.P weighs 0.09 g]

Answer 1

Pressure P₁ = 380 mm $\mathrm{Hg}$ ; Pressure P₂ = 760 mm $\mathrm{Hg}$

Using the gas equation,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

V₁ = 360 cm³ ; V₂ = X cm³

$$\begin{gathered} V_2=\frac{P_1{V}_1{T}_2}{T_1{P}_2} \\ =\frac{380\times 360\times 273}{360\times 760} \\ =136.5c{m}^3 \end{gathered}$$

T₁ = 87 + 273 K

T₂ = 273K

So, 136.5 cm³ of the gas at S.T.P. weighs = 0.546 g

$\therefore$1000 cm³ of the gas at S.T.P weighs = $\frac{0.546}{136.5}\times 1000=4g$

Vapour density $$\begin{gathered} =\frac{weightof1000mlgas}{weightof1000ml{\mathrm{H}}_2} \\ =\frac{4}{0.09} \\ =44.44 \end{gathered}$$

Relative molecular mass of gas = 2 x Vapour density

$$\begin{gathered} =2\times 44.44 \\ =88.88g \end{gathered}$$

Therefore, Relative molecular mass of a gas is 88.88g.